> Full-text translation from Chinese. The original remains authoritative for its research claims; this translation is not independent mathematical verification.

# MCC-OE-28 — Reconstructed Edition
## Root-6217 Replay Contract, Publication Debt Ledger and AMRAL LinkBack

**Version:** reconstructed-v1 · 2026-10-08  
**Nature:** At Neo.K's direction, an editorial reconstruction based on the surviving MCC-OE-27, LESR handoff and 09V snapshot. The original Paper 28 and conversation have not been recovered; the tables and contracts below were created for this reconstruction and are not presented as the original manuscript.

## 0. Continuation point

Sections 62–67 of MCC-OE-27 already identify the next node's title and five work lanes: authority-promotion contracts, local-interval replay, replay of closed tail parent cells, persistent state for the remaining parent cells, and links back to AMRAL's global responsibility graph. This edition expands those five items into an actionable handoff contract.

This edition adds no geometric lower bound for root-6217. The local thresholds remain approximately A0 = 0.83498611 and tail A_ref = 0.8349865; neither can thereby be promoted to a global Lebesgue lower bound of 0.835.

## 1. First distinguish two observed versions

| Source | Hard-core parent cells | Reported closed cells | Evidence level |
|---|---:|---|---|
| Manifest embedded in the 2026-09-24 09V snapshot | 29 | 1, 13, 45, 47, 95, 143, 169, 178, 186 | Nine have snapshot-manifest and state-file support; their complete numerical certificates still require replay |
| Final LESR handoff and MCC-OE-27 | 29 | 0 plus the nine above | Ten belong to the later textual ledger; parent 0's final closure certificate has not been recovered |

The later list of remaining cells is

```text
46,63,81,92,93,94,124,125,128,129,131,142,150,152,159,160,161,168,177
```

The earlier 9/29 state files must not be rewritten as the later 10/29 state. Preserve the supersedes relationship and each version's artifact hash. Parent cells 129 and 131 must also be identified together with their target and clipping interval; closure for an original target does not automatically establish closure for the tail's new target.

## 2. Lane A: authority-promotion contract

Retain the research-state progression

```text
RESEARCH-CLOSED → LOCAL-REPLAY-PASSED → PUBLICATION-CERTIFIED
```

Every promotion must include, at minimum: proposition ID, target, parameter domain, arithmetic backend and error contract, input and program hashes, output-certificate hash, replay operator and execution version, and failed or missing obligations.

`LOCAL-REPLAY-PASSED` requires actual replay with matching results; `PUBLICATION-CERTIFIED` additionally requires valid coverage by every finite leaf, complete root/branch enumeration, outward error control and provenance for independent checking. This text performs none of these promotions.

## 3. Lane B: local [0,0.003] replay checklist

Keep the microscopic segment, B01–B11 bridge cells and finite parent-cell composition as separate propositions within the local replay scope. For every cell, record

```text
claim_id / target_id / rho_interval / parameter_box
method / authority / assumptions
inputs / program / certificate / hashes
result / unresolved_obligations
```

Existing research-interval checks and floating-point error contracts must be identified without alteration. Cell centres, sample points or a summary PASS cannot replace a certificate covering the entire cell.

## 4. Lane C: replay contract for closed tail parent cells

For the tail [0.003,π/120], every parent cell needs its own clipped domain, A_ref, binary subdivision tree, unprocessed queue, leaf types and minimum margin. Replay must check whether the tree covers the entire target, whether NOT-F3 and A leaves satisfy their respective conditions, and whether backend assumptions hold.

This reconstructed edition first introduces three states: `AVAILABLE_SNAPSHOT`, `TEXT_REPORTED_ONLY` and `MISSING_CERTIFICATE`. Parent 0's later state has the latter two designations; its appearance in the final handoff list cannot justify inventing a closure certificate.

## 5. Lane D: persistent state for the remaining nineteen cells

Suggested state format:

```json
{
  "parent_id": 46,
  "target_id": "root6217-tail-aref",
  "status": "OPEN",
  "queue_artifact": null,
  "checkpoint_sha256": null,
  "backend": null,
  "verified_leaf_count": null,
  "remaining_obligations": ["resume from an identified checkpoint"]
}
```

`null` means an unrecovered input, not zero. State updates require new execution records and certificates; ledgers with old root IDs, old targets or different backends cannot simply be added together.

## 6. Lane E: links back to AMRAL's responsibility graph

Every local result links back to the LESR source, corresponding MCC-OE node, replay package and parent Lebesgue problem. Relationships should include `depends_on`, `supersedes`, `replays`, `reported_by` and `open_obligation`.

Local research closure, replayable certificates and global geometric implications are distinct nodes. The last still requires a sufficiency proof connecting the local target to all diameter-one convex bodies; this edition supplies no such global arrow.

## 7. Deliverables and material still to be recovered

This edition restores the next-node structure specified by MCC-OE-27 and makes the 9/29 versus 10/29 distinction traceable. It completes no deep DFS search and does not promote the authority of the entire tail.

Still missing: parent 0's later certificate, the remaining nineteen cells, an independent publication-grade numerical audit, positive rotation, all root-6217 shapes, and the global Lebesgue problem.

## Sources

- MCC_OE_27_Root6217_Residual_Ledger_Reconciliation_and_Hybrid_Certificate_Atlas_v0.1_2026-09-24.md, especially Sections 62–68.
- LESR_Root6217_Local_Verification_and_Series_Integration_Handoff_v0.1.md, Sections 11–14 and 26.
- The published LESR_09V_Tail_Campaign_Snapshot_2026-09-24_manifest.json and eight checkpoints.

===END OF RECONSTRUCTED EDITION===